In this chapter we present some results related to Newton's method in order to extend the solvability of optimal shape design problems. Moreover, some numerical examples are also presented in the chapter.

In this work we study a family of shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. ...

We consider an optimization problem with volume constraint for an energy functional associated to an inhomogeneous operator with nonstandard growth. By studying an auxiliary penalized problem, we prove existence and ...

In this manuscript we study the following optimization problem: given a bounded and regular domain Ω⊂RN we look for an optimal shape for the “W−vanishing window” on the boundary with prescribed measure over all admissible ...

In this paper we study the asymptotic behavior of some optimal design problems related to nonlinear Steklov eigenvalues, under irregular (but diffeomorphic) perturbations of the domain.

In this paper we study two optimal design problems associated to fractional Sobolev spaces Ws,p(Ω). Then we find a relationship between these two problems and finally we investigate the convergence when s↑1.

Shape optimization seeks to optimize the shape of a region where certain partial differential equation is posed such that a functional of its solution is minimized/maximized. In this thesis we give an introduction to ...